Abstract
In this paper, a novel hybrid optimization approach, namely, gravitational particle swarm optimization algorithm (GPSOA), is introduced based on particle swarm optimization (PSO) and gravitational search algorithm (GSA) to solve combined economic and emission dispatch (CEED) problem considering wind power availability for the wind-thermal power system. The proposed algorithm shows an interesting hybrid strategy and perfectly integrates the collective behaviors of PSO with the Newtonian gravitation laws of GSA. GPSOA updates particle’s velocity caused by the dependent random cooperation of GSA gravitational acceleration and PSO velocity. To describe the stochastic characteristics of wind speed and output power, Weibull-based probability density function (PDF) is utilized. The CEED model employed consists of the fuel cost objective and emission-level target produced by conventional thermal generators and the operational cost generated by wind turbines. The effectiveness of the suggested GPSOA is tested on the conventional thermal generator system and the modified wind-thermal power system. Results of GPSOA-based CEED problems by means of the optimal fuel cost, emission value, and best compromise solution are compared with the original PSO, GSA, and other state-of-the-art optimization approaches to reveal that the introduced GPSOA exhibits competitive performance improvements in finding lower fuel cost and emission cost and best compromise solution.
Highlights
(a) e performance of the newly proposed gravitational particle swarm optimization algorithm (GPSOA), as an optimization tool in solving wind power-integrated combined economic and emission dispatch (CEED) problems, is investigated on different conventional and wind-thermal power test systems and the obtained results are presented
The stochastic characteristics of wind speed and output power are described by a Weibull-based probability density function (PDF) in Section 2.1. us, the operational cost caused by underestimation and overestimation of wind power is computed in Section 2.2 using a closed-form equation by means of the incomplete gamma function (IGF)
The proposed GPSOA is carried out to comprehensively investigate the CEED problem of three different test cases, and they are given as follows: Case 1. e conventional IEEE 30-bus test system including six thermal generators and neglecting wind power penetration was studied as the benchmark to verify the performance of the proposed GPSOA. e system transmission loss PL is considered. e results are compared with those obtained by the existing algorithms to demonstrate the superiority performance of the suggested algorithm. e line data, bus data, and fuel cost and emission coefficients for standard IEEE 30-bus test systems are taken from [46, 47] and the B-loss coefficients from [48]
Summary
(a) e performance of the newly proposed GPSOA, as an optimization tool in solving wind power-integrated CEED problems, is investigated on different conventional and wind-thermal power test systems and the obtained results are presented. (b) e best results obtained from the solution of the CEED problems of test systems by adopting this proposed approach are compared to those published in the recent literature. The objective formulation of the CEED problem with wind power incorporation and its constraints are described in the following. When ignoring some minor nonlinear factors, a simplified linear piecewise function is given to describe the actual relationship between them, as shown in the following equation: w
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